Gear transmission systems typically include two or more gears rotationally engaged with each other. In order for two gears to be properly engaged with each other, the gears should have substantially the same diametral pitch. The diametral pitch is a measure of the angular distance between adjacent teeth of a gear. The diametral pitch is typically represented as the ratio of the number of teeth to the diameter of the gear. This concept will be further explained with reference to FIG. 1.
FIG. 1 illustrates an exemplary gear transmission system 100 to illustrate a general concept of the pertinent art. The gear transmission system 100 consists of a first gear 110 rotationally engaged with a second gear 120. The first gear 110 has a diameter D1 and N1 number of teeth 112. The second gear 120 has a diameter D2 and N2 number of teeth 122. In this example, the diameter D1 of the first gear 110 is larger than the diameter D2 of the second gear 120.
As previously discussed, in order for the first and second gears 110 and 120 to rotationally engage properly, the diametral pitch of the first gear 110 should be substantially the same as the diametral pitch of the second gear 120. The diametral pitch is the ratio of the number of teeth to the diameter of the gear. Accordingly, the following relationship holds:
                                          N            1                                D            1                          ≅                              N            2                                D            2                                              Equation  1            
Such a gear transmission system 100 operates well as long as the diametral pitches of the first and second gears 110 and 120 remain fixed and substantially the same.
However, there may be gear transmission systems that require the movement of such gears in a manner that causes the diametral pitches of engaging gears to depart from the relationship given in Equation 1. Such a system is described with reference to FIG. 2.
FIG. 2 illustrates another exemplary gear transmission system 200 to illustrate a problem to be solved by the invention. The gear transmission system 200 consists of a first gear 210 rotationally engaged with a second gear 220. In this example, the first gear 210 rotates about a rotational axis substantially orthogonal to the rotational axis of the second gear 220. Also in this example, the second gear 220 is required to move radially with respect to the first gear 210 such that the teeth 222 of the second gear 220 can engage with a set of teeth 212 situated along a relatively small circumference of the first gear 210 and with another set of teeth 214 situated along a relatively larger circumference of the first gear 210.
This movement 230 has the effect of changing the gear ratio of the first and second gears 210 and 220, which may be a requirement of many transmission systems. In this example, the first gear is shown to have two sets of teeth 212 and 214. However, it shall be understood that the first gear 210 may have many sets of teeth situated at various circumferences between sets 212 and 214. This allows the gradual change of the gear ratio of the first and second gears 210 and 220.
A problem with this system 200 has to do with the diametral pitch requirement for the first gear 210 to rotationally engage properly with the second gear 220 at all of the sets of teeth from the inner teeth set 212 to the outer teeth set 214. As previously discussed, in order for engaging gears to rotate properly with each other, the diametral pitches of the gears should be substantially the same. In this example, the diametral pitch of the second gear 220 should be substantially the same as the diametral pitch corresponding to the sets of teeth 212 and 214 of the first gear 210. Accordingly, the following relationship holds:
                                          N            3                                D            3                          ≅                              N            4                                D            4                          ≅                              N            5                                D            5                                              Equation  2            
Because the diameter D3 of the inner teeth set 212 is smaller than the diameter D4 of the outer teeth set 214, the number of teeth N3 of the inner teeth set 212 should be smaller than the number of teeth N4 of the outer teeth set 214 in order for Equation 2 to hold. If there are plurality of circumferential teeth sets between the inner and outer teeth sets 212 and 214, then the number of teeth for those sets increases with their circumferences according to Equation 2. Because of the varying quantities of teeth for the various sets, it is difficult to align the teeth in the radial direction throughout the entire circumference in order to provide a path 230 in which the second gear 230 could rotate freely substantially without interference or backlash.